IE582-Assignment 2
Deniz Sezin Ayvaz - IE582 - Fall 2018
26 October 2018
TASK 1 and TASK 2
In these tasks, we are asked to choose 5 bookmakers and and apply PCA with their odds data.
For example, for Pinnacle, the first two components capture 92% of the total variance.
Also, away win odd is the feature that captures the variability the most.
## Warning: package 'dplyr' was built under R version 3.4.4##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union## Loading required package: data.table## Warning: package 'data.table' was built under R version 3.4.4##
## Attaching package: 'data.table'## The following objects are masked from 'package:dplyr':
##
## between, first, last## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 0.1825755 0.05393369 0.012518614 0.006318502
## Proportion of Variance 0.9139673 0.07975649 0.004296931 0.001094647
## Cumulative Proportion 0.9139673 0.99372380 0.998020727 0.999115374
## Comp.5 Comp.6 Comp.7
## Standard deviation 0.0055127591 1.365384e-03 9.428989e-05
## Proportion of Variance 0.0008332664 5.111586e-05 2.437677e-07
## Cumulative Proportion 0.9999486404 9.999998e-01 1.000000e+00##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7
## odd1_Pinnacle_NA 0.194 0.916 0.240 0.164 -0.192
## odd2_Pinnacle_NA -0.957 0.166 0.132 -0.173
## oddX_Pinnacle_NA -0.214 0.371 -0.387 -0.422 0.690 0.113
## over_Pinnacle_0.5 0.108 -0.992
## over_Pinnacle_2.5 0.668 -0.214 0.390 -0.590
## under_Pinnacle_0.5 -0.848 -0.506 -0.127
## under_Pinnacle_2.5 -0.559 -0.214 -0.796
##
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7
## SS loadings 1.000 1.000 1.000 1.000 1.000 1.000 1.000
## Proportion Var 0.143 0.143 0.143 0.143 0.143 0.143 0.143
## Cumulative Var 0.143 0.286 0.429 0.571 0.714 0.857 1.000
## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 0.1390548 0.08641774 0.04472684 0.009121567
## Proportion of Variance 0.6681044 0.25803472 0.06912080 0.002874824
## Cumulative Proportion 0.6681044 0.92613914 0.99525994 0.998134766
## Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 0.006217179 0.0028650498 0.0023409420 1.222277e-03
## Proportion of Variance 0.001335547 0.0002836199 0.0001893449 5.161925e-05
## Cumulative Proportion 0.999470313 0.9997539325 0.9999432774 9.999949e-01
## Comp.9
## Standard deviation 3.843178e-04
## Proportion of Variance 5.103326e-06
## Cumulative Proportion 1.000000e+00##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8
## NO_Betway_NA 0.109 -0.300 -0.462 -0.417 0.359 0.616
## YES_Betway_NA -0.103 0.293 0.391 0.195 -0.325 0.778
## odd1_Betway_NA -0.234 0.505 -0.772 0.196 -0.231
## odd2_Betway_NA 0.799 -0.373 -0.368 0.186 -0.224
## oddX_Betway_NA 0.208 0.103 -0.337 -0.701 0.552 0.190
## over_Betway_0.5 -0.144
## over_Betway_2.5 0.307 0.414 -0.834 -0.108
## under_Betway_0.5 0.507 0.763 0.362 0.153
## under_Betway_2.5 -0.378 -0.217 -0.261 -0.850
## Comp.9
## NO_Betway_NA
## YES_Betway_NA
## odd1_Betway_NA
## odd2_Betway_NA
## oddX_Betway_NA
## over_Betway_0.5 -0.986
## over_Betway_2.5 0.135
## under_Betway_0.5
## under_Betway_2.5
##
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8
## SS loadings 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
## Proportion Var 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111
## Cumulative Var 0.111 0.222 0.333 0.444 0.556 0.667 0.778 0.889
## Comp.9
## SS loadings 1.000
## Proportion Var 0.111
## Cumulative Var 1.000
## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 0.1823609 0.1021055 0.04409562 0.007483578
## Proportion of Variance 0.7272582 0.2279942 0.04252224 0.001224740
## Cumulative Proportion 0.7272582 0.9552524 0.99777462 0.998999359
## Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 0.0056889942 0.0028326541 1.753611e-03 1.494435e-03
## Proportion of Variance 0.0007077767 0.0001754738 6.724989e-05 4.884043e-05
## Cumulative Proportion 0.9997071360 0.9998826098 9.999499e-01 9.999987e-01
## Comp.9
## Standard deviation 2.438038e-04
## Proportion of Variance 1.299889e-06
## Cumulative Proportion 1.000000e+00##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8
## NO_Unibet_NA 0.115 -0.349 -0.358 -0.492 0.380 0.591
## YES_Unibet_NA -0.104 0.348 0.262 0.197 -0.373 0.788
## odd1_Unibet_NA 0.576 -0.761 -0.272
## odd2_Unibet_NA 0.608 -0.613 -0.419 -0.266
## oddX_Unibet_NA 0.208 -0.318 -0.489 0.749 0.225
## over_Unibet_0.5
## over_Unibet_2.5 0.574 0.309 -0.732 -0.136
## under_Unibet_0.5 0.759 0.535 0.343 0.136
## under_Unibet_2.5 -0.394 -0.412 -0.811
## Comp.9
## NO_Unibet_NA
## YES_Unibet_NA
## odd1_Unibet_NA
## odd2_Unibet_NA
## oddX_Unibet_NA
## over_Unibet_0.5 -0.995
## over_Unibet_2.5
## under_Unibet_0.5
## under_Unibet_2.5
##
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8
## SS loadings 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
## Proportion Var 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111
## Cumulative Var 0.111 0.222 0.333 0.444 0.556 0.667 0.778 0.889
## Comp.9
## SS loadings 1.000
## Proportion Var 0.111
## Cumulative Var 1.000
## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 0.1515605 0.0742054 0.03799709 0.007034968
## Proportion of Variance 0.7652335 0.1834395 0.04809748 0.001648717
## Cumulative Proportion 0.7652335 0.9486730 0.99677046 0.998419173
## Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 0.005917478 0.0026733107 0.0018943852 0.0012914873
## Proportion of Variance 0.001166528 0.0002380788 0.0001195524 0.0000555651
## Cumulative Proportion 0.999585701 0.9998237797 0.9999433321 0.9999988972
## Comp.9
## Standard deviation 1.819412e-04
## Proportion of Variance 1.102768e-06
## Cumulative Proportion 1.000000e+00##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8
## NO_bwin_NA -0.148 0.299 -0.390 -0.564 0.280 0.583
## YES_bwin_NA 0.138 -0.216 0.302 0.358 -0.240 0.810
## odd1_bwin_NA 0.214 -0.662 0.652 0.291
## odd2_bwin_NA -0.841 0.243 0.390 0.281
## oddX_bwin_NA -0.244 -0.232 0.228 -0.799 -0.396 -0.139 0.139
## over_bwin_0.5
## over_bwin_2.5 -0.230 0.625 -0.708 -0.174
## under_bwin_0.5 -0.427 -0.657 -0.565 0.246
## under_bwin_2.5 -0.376 -0.147 -0.898
## Comp.9
## NO_bwin_NA
## YES_bwin_NA
## odd1_bwin_NA
## odd2_bwin_NA
## oddX_bwin_NA
## over_bwin_0.5 -0.992
## over_bwin_2.5 0.109
## under_bwin_0.5
## under_bwin_2.5
##
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8
## SS loadings 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
## Proportion Var 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111
## Cumulative Var 0.111 0.222 0.333 0.444 0.556 0.667 0.778 0.889
## Comp.9
## SS loadings 1.000
## Proportion Var 0.111
## Cumulative Var 1.000
## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 0.2032587 0.1386602 0.06286807 0.009788170
## Proportion of Variance 0.6390488 0.2973987 0.06113583 0.001481967
## Cumulative Proportion 0.6390488 0.9364475 0.99758331 0.999065276
## Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 0.0063465469 0.0034916697 0.002023776 1.789684e-03
## Proportion of Variance 0.0006230323 0.0001885827 0.000063352 4.954368e-05
## Cumulative Proportion 0.9996883080 0.9998768907 0.999940243 9.999898e-01
## Comp.9
## Standard deviation 8.125913e-04
## Proportion of Variance 1.021363e-05
## Cumulative Proportion 1.000000e+00##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8
## NO_Betsafe_NA 0.124 0.452 -0.252 -0.519 0.666
## YES_Betsafe_NA -0.113 -0.420 0.103 0.816 0.355
## odd1_Betsafe_NA 0.111 0.565 -0.771 -0.267
## odd2_Betsafe_NA -0.636 -0.586 -0.428 -0.257
## oddX_Betsafe_NA -0.203 -0.287 0.159 0.884 -0.179 -0.136 0.128
## over_Betsafe_0.5 -0.106
## over_Betsafe_2.5 -0.633 -0.679 -0.325 -0.129
## under_Betsafe_0.5 -0.732 0.573 0.329 -0.152
## under_Betsafe_2.5 0.406 -0.470 0.447 -0.626
## Comp.9
## NO_Betsafe_NA
## YES_Betsafe_NA
## odd1_Betsafe_NA
## odd2_Betsafe_NA
## oddX_Betsafe_NA
## over_Betsafe_0.5 0.988
## over_Betsafe_2.5
## under_Betsafe_0.5
## under_Betsafe_2.5 -0.120
##
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8
## SS loadings 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
## Proportion Var 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111
## Cumulative Var 0.111 0.222 0.333 0.444 0.556 0.667 0.778 0.889
## Comp.9
## SS loadings 1.000
## Proportion Var 0.111
## Cumulative Var 1.000
Comments:
It is not easy to distinguish over/under 2.5 situation by looking at the PCA results. On the other hand, home/away/tie situations can be distinguished easier in all 5 bookmakers’ PCA plots (V-shaped and colors are not distributed homogenic)
There is no significant difference between MDS with Euclidean distance and PCA results.
MDS with Manhattan distance performs better than MDS with Euclidean distance. (Sharper V-shaped)
TASK 3
Below are the image I chose, RGB channels of it, its noised version, and its channels.
## Importance of components:
## Comp.1 Comp.2 Comp.3
## Standard deviation 0.4530941 0.09680673 0.04993670
## Proportion of Variance 0.9453617 0.04315512 0.01148315
## Cumulative Proportion 0.9453617 0.98851685 1.00000000##
## Loadings:
## Comp.1 Comp.2 Comp.3
## [1,] -0.572 0.707 0.415
## [2,] -0.587 -0.810
## [3,] -0.572 -0.707 0.415
##
## Comp.1 Comp.2 Comp.3
## SS loadings 1.000 1.000 1.000
## Proportion Var 0.333 0.333 0.333
## Cumulative Var 0.333 0.667 1.000I used first, second and third components of PCA consequently, to reconstruct the image. First component is better at capturing the variance, as can be seen below.
I plotted first, second and third components of PCA as 3 by 3 images.
APPENDIX setwd(“C:/Users/dsa/Desktop/582 Dosyalar”)
library(jpeg) library(dplyr) require(data.table)
TASK1 and TASK2
matches=readRDS(“df9b1196-e3cf-4cc7-9159-f236fe738215_matches.rds”)
odd_details=readRDS(“df9b1196-e3cf-4cc7-9159-f236fe738215_odd_details.rds”)
matches=unique(matches)
matches[,c(“HomeGoals”,“AwayGoals”):=tstrsplit(score,‘:’)]
transform characters to numeric for scores
matches\(HomeGoals=as.numeric(matches\)HomeGoals) matches[,AwayGoals:=as.numeric(AwayGoals)]
calculate total goals
matches[,TotalGoals:=HomeGoals+AwayGoals]
mark over under
matches[,IsOver:=0] matches[TotalGoals>2,IsOver:=1]
mark match outcome
matches[,Result:=2] #tie matches[AwayGoals>HomeGoals,Result:=1] #away matches[AwayGoals<HomeGoals,Result:=0] #home
order data in ascending date
odds_ordered=odd_details[order(matchId,oddtype,bookmaker,date)]
take final odds
odds_ordered_final=odds_ordered[,list(final_odd=odd[.N]), by=list(matchId,oddtype,bookmaker,totalhandicap)]
for pinnacle
bookmaker_odds=odds_ordered_final[bookmaker==‘Pinnacle’ & (is.na(totalhandicap) | totalhandicap == 2.5 | totalhandicap == 0.5) & (oddtype %in% c(“odd1”,“odd2”,“oddX”,“YES”,“NO”,“over”,“under”))]
bookmaker_wide=dcast(bookmaker_odds, matchId~oddtype+bookmaker+totalhandicap, value.var=‘final_odd’)
merged_matches=merge(matches,bookmaker_wide,by=‘matchId’)
merged_matches=merged_matches[complete.cases(merged_matches)]
Result1<-as.numeric(merged_matches\(IsOver) Result2<-merged_matches\)Result merged_matches<-merged_matches[,-c(1:12)]
scaling
merged_matches<-((merged_matches-min(merged_matches))/(max(merged_matches)-min(merged_matches)))
pca<-princomp(merged_matches) summary(pca) pca$loadings
mds_data<-dist(merged_matches,method = “euclidean”) mds_data<-cmdscale(mds_data) mds_data_manhattan<-dist(merged_matches,method = “manhattan”) mds_data_manhattan<-cmdscale(mds_data_manhattan)
par(mfrow=c(2,2)) plot(pca\(scores[,1],pca\)scores[,2],main=‘PCA for Pinnacle’,col=Result1+1,pch=“.”,cex=6,xlab=“Comp1”,ylab=“Comp2”) legend(“topleft”, legend=c(“Under 2.5”,“Over 2.5”),col=c(1,2),pch = “.”,pt.cex = 6) plot(pca\(scores[,1],pca\)scores[,2],main=‘PCA for Pinnacle’,col=Result2+1,pch=“.”,cex=6,xlab=“Comp1”,ylab=“Comp2”) legend(“topleft”, legend=c(“Home”,“Away”,“Tie”),col=c(1,2,3), pch = “.”,pt.cex = 6)
plot(mds_data[,1],mds_data[,2],main=‘MDS with Euclidean Dist. for Pinnacle’,xlab=‘’, ylab=’’,col=Result1+1,pch=“.”,cex=7) legend(“bottomleft”, legend=c(“Under 2.5”,“Over 2.5”),col=c(1,2), pch = “.”,pt.cex = 6)
plot(mds_data_manhattan[,1],mds_data_manhattan[,2],main=‘MDS with Manhattan Dist. for Pinnacle’,xlab=‘’,cex.main = 1, ylab=’’,col=Result1+1,pch=“.”,cex=6) legend(“bottomleft”, legend=c(“Under 2.5”,“Over 2.5”),col=c(1,2), pch = “.”,pt.cex = 6)
for betway
bookmaker_odds=odds_ordered_final[bookmaker==‘Betway’ & (is.na(totalhandicap) | totalhandicap == 2.5 | totalhandicap == 0.5) & (oddtype %in% c(“odd1”,“odd2”,“oddX”,“YES”,“NO”,“over”,“under”))]
bookmaker_wide=dcast(bookmaker_odds, matchId~oddtype+bookmaker+totalhandicap, value.var=‘final_odd’)
merged_matches=merge(matches,bookmaker_wide,by=‘matchId’)
merged_matches=merged_matches[complete.cases(merged_matches)]
Result1<-as.numeric(merged_matches\(IsOver) Result2<-merged_matches\)Result merged_matches<-merged_matches[,-c(1:12)]
scaling
merged_matches<-((merged_matches-min(merged_matches))/(max(merged_matches)-min(merged_matches)))
pca<-princomp(merged_matches) summary(pca) pca$loadings
mds_data<-dist(merged_matches,method = “euclidean”) mds_data<-cmdscale(mds_data) mds_data_manhattan<-dist(merged_matches,method = “manhattan”) mds_data_manhattan<-cmdscale(mds_data_manhattan)
par(mfrow=c(2,2)) plot(pca\(scores[,1],pca\)scores[,2],main=‘PCA for Betway’,col=Result1+1,pch=“.”,cex=6,xlab=“Comp1”,ylab=“Comp2”) legend(“topleft”, legend=c(“Under 2.5”,“Over 2.5”),col=c(1,2),pch = “.”,pt.cex = 6) plot(pca\(scores[,1],pca\)scores[,2],main=‘PCA for Betway’,col=Result2+1,pch=“.”,cex=6,xlab=“Comp1”,ylab=“Comp2”) legend(“topleft”, legend=c(“Home”,“Away”,“Tie”),col=c(1,2,3), pch = “.”,pt.cex = 6)
plot(mds_data[,1],mds_data[,2],main=‘MDS with Euclidean Dist. for Betway’,xlab=‘’, ylab=’’,col=Result1+1,pch=“.”,cex=7) legend(“bottomleft”, legend=c(“Under 2.5”,“Over 2.5”),col=c(1,2), pch = “.”,pt.cex = 6)
plot(mds_data_manhattan[,1],mds_data_manhattan[,2],main=‘MDS with Manhattan Dist. for Betway’,xlab=‘’,cex.main = 1, ylab=’’,col=Result1+1,pch=“.”,cex=6) legend(“bottomleft”, legend=c(“Under 2.5”,“Over 2.5”),col=c(1,2), pch = “.”,pt.cex = 6)
for Unibet
bookmaker_odds=odds_ordered_final[bookmaker==‘Unibet’ & (is.na(totalhandicap) | totalhandicap == 2.5 | totalhandicap == 0.5) & (oddtype %in% c(“odd1”,“odd2”,“oddX”,“YES”,“NO”,“over”,“under”))]
bookmaker_wide=dcast(bookmaker_odds, matchId~oddtype+bookmaker+totalhandicap, value.var=‘final_odd’)
merged_matches=merge(matches,bookmaker_wide,by=‘matchId’)
merged_matches=merged_matches[complete.cases(merged_matches)]
Result1<-as.numeric(merged_matches\(IsOver) Result2<-merged_matches\)Result merged_matches<-merged_matches[,-c(1:12)]
scaling
merged_matches<-((merged_matches-min(merged_matches))/(max(merged_matches)-min(merged_matches)))
pca<-princomp(merged_matches) summary(pca) pca$loadings
mds_data<-dist(merged_matches,method = “euclidean”) mds_data<-cmdscale(mds_data) mds_data_manhattan<-dist(merged_matches,method = “manhattan”) mds_data_manhattan<-cmdscale(mds_data_manhattan)
par(mfrow=c(2,2)) plot(pca\(scores[,1],pca\)scores[,2],main=‘PCA for Unibet’,col=Result1+1,pch=“.”,cex=6,xlab=“Comp1”,ylab=“Comp2”) legend(“topleft”, legend=c(“Under 2.5”,“Over 2.5”),col=c(1,2),pch = “.”,pt.cex = 6) plot(pca\(scores[,1],pca\)scores[,2],main=‘PCA for Unibet’,col=Result2+1,pch=“.”,cex=6,xlab=“Comp1”,ylab=“Comp2”) legend(“topleft”, legend=c(“Home”,“Away”,“Tie”),col=c(1,2,3), pch = “.”,pt.cex = 6)
plot(mds_data[,1],mds_data[,2],main=‘MDS with Euclidean Dist. for Unibet’,xlab=‘’, ylab=’’,col=Result1+1,pch=“.”,cex=7) legend(“bottomleft”, legend=c(“Under 2.5”,“Over 2.5”),col=c(1,2), pch = “.”,pt.cex = 6)
plot(mds_data_manhattan[,1],mds_data_manhattan[,2],main=‘MDS with Manhattan Dist. for Unibet’,xlab=‘’,cex.main = 1, ylab=’’,col=Result1+1,pch=“.”,cex=6) legend(“bottomleft”, legend=c(“Under 2.5”,“Over 2.5”),col=c(1,2), pch = “.”,pt.cex = 6)
for bwin
bookmaker_odds=odds_ordered_final[bookmaker==‘bwin’ & (is.na(totalhandicap) | totalhandicap == 2.5 | totalhandicap == 0.5) & (oddtype %in% c(“odd1”,“odd2”,“oddX”,“YES”,“NO”,“over”,“under”))]
bookmaker_wide=dcast(bookmaker_odds, matchId~oddtype+bookmaker+totalhandicap, value.var=‘final_odd’)
merged_matches=merge(matches,bookmaker_wide,by=‘matchId’)
merged_matches=merged_matches[complete.cases(merged_matches)]
Result1<-as.numeric(merged_matches\(IsOver) Result2<-merged_matches\)Result merged_matches<-merged_matches[,-c(1:12)]
scaling
merged_matches<-((merged_matches-min(merged_matches))/(max(merged_matches)-min(merged_matches)))
pca<-princomp(merged_matches) summary(pca) pca$loadings
mds_data<-dist(merged_matches,method = “euclidean”) mds_data<-cmdscale(mds_data) mds_data_manhattan<-dist(merged_matches,method = “manhattan”) mds_data_manhattan<-cmdscale(mds_data_manhattan)
par(mfrow=c(2,2)) plot(pca\(scores[,1],pca\)scores[,2],main=‘PCA for bwin’,col=Result1+1,pch=“.”,cex=6,xlab=“Comp1”,ylab=“Comp2”) legend(“topleft”, legend=c(“Under 2.5”,“Over 2.5”),col=c(1,2),pch = “.”,pt.cex = 6) plot(pca\(scores[,1],pca\)scores[,2],main=‘PCA for bwin’,col=Result2+1,pch=“.”,cex=6,xlab=“Comp1”,ylab=“Comp2”) legend(“topleft”, legend=c(“Home”,“Away”,“Tie”),col=c(1,2,3), pch = “.”,pt.cex = 6)
plot(mds_data[,1],mds_data[,2],main=‘MDS with Euclidean Dist. for bwin’,xlab=‘’, ylab=’’,col=Result1+1,pch=“.”,cex=7) legend(“bottomleft”, legend=c(“Under 2.5”,“Over 2.5”),col=c(1,2), pch = “.”,pt.cex = 6)
plot(mds_data_manhattan[,1],mds_data_manhattan[,2],main=‘MDS with Manhattan Dist. for bwin’,xlab=‘’,cex.main = 1, ylab=’’,col=Result1+1,pch=“.”,cex=6) legend(“bottomleft”, legend=c(“Under 2.5”,“Over 2.5”),col=c(1,2), pch = “.”,pt.cex = 6)
for Betsafe
bookmaker_odds=odds_ordered_final[bookmaker==‘Betsafe’ & (is.na(totalhandicap) | totalhandicap == 2.5 | totalhandicap == 0.5) & (oddtype %in% c(“odd1”,“odd2”,“oddX”,“YES”,“NO”,“over”,“under”))]
bookmaker_wide=dcast(bookmaker_odds, matchId~oddtype+bookmaker+totalhandicap, value.var=‘final_odd’)
merged_matches=merge(matches,bookmaker_wide,by=‘matchId’)
merged_matches=merged_matches[complete.cases(merged_matches)]
Result1<-as.numeric(merged_matches\(IsOver) Result2<-merged_matches\)Result merged_matches<-merged_matches[,-c(1:12)]
scaling
merged_matches<-((merged_matches-min(merged_matches))/(max(merged_matches)-min(merged_matches)))
pca<-princomp(merged_matches) summary(pca) pca$loadings mds_data<-dist(merged_matches,method = “euclidean”) mds_data<-cmdscale(mds_data) mds_data_manhattan<-dist(merged_matches,method = “manhattan”) mds_data_manhattan<-cmdscale(mds_data_manhattan)
par(mfrow=c(2,2)) plot(pca\(scores[,1],pca\)scores[,2],main=‘PCA for Betsafe’,col=Result1+1,pch=“.”,cex=6,xlab=“Comp1”,ylab=“Comp2”) legend(“topleft”, legend=c(“Under 2.5”,“Over 2.5”),col=c(1,2),pch = “.”,pt.cex = 6) plot(pca\(scores[,1],pca\)scores[,2],main=‘PCA for Betsafe’,col=Result2+1,pch=“.”,cex=6,xlab=“Comp1”,ylab=“Comp2”) legend(“topleft”, legend=c(“Home”,“Away”,“Tie”),col=c(1,2,3), pch = “.”,pt.cex = 6)
plot(mds_data[,1],mds_data[,2],main=‘MDS with Euclidean Dist. for Betsafe’,xlab=‘’, ylab=’’,col=Result1+1,pch=“.”,cex=7) legend(“bottomleft”, legend=c(“Under 2.5”,“Over 2.5”),col=c(1,2), pch = “.”,pt.cex = 6)
plot(mds_data_manhattan[,1],mds_data_manhattan[,2],main=‘MDS with Manhattan Dist. for Betsafe’,xlab=‘’,cex.main = 1, ylab=’’,col=Result1+1,pch=“.”,cex=6) legend(“bottomleft”, legend=c(“Under 2.5”,“Over 2.5”),col=c(1,2), pch = “.”,pt.cex = 6)
task3
homework_image<-readJPEG(“image512.jpg”) par(mfrow=c(1,1))
display image
plot(NA,xlim=c(0,nrow(homework_image)),ylim=c(0,ncol(homework_image))) rasterImage(homework_image,0,0,nrow(homework_image),ncol(homework_image),interpolate=TRUE)
display each channel
par(mfrow=c(1,3)) image(homework_image[,,1],col=rgb(c(0:255)/255,0,0),useRaster = TRUE,axes=FALSE) image(homework_image[,,2],col=rgb(0,c(0:255)/255,0),useRaster = TRUE,axes=FALSE) image(homework_image[,,3],col=rgb(0,0,c(0:255)/255),useRaster = TRUE,axes=FALSE)
add noise
hw_image_initial<-homework_image
for(k in 1:3){ for(i in 1:512){ for(j in 1:512){ homework_image[i,j,k]<- homework_image[i,j,k]+runif(1,0,0.1) } }
}
scaling
homework_image<-homework_image/max(homework_image)
par(mfrow=c(1,1)) plot(NA,xlim=c(0,nrow(homework_image)),ylim=c(0,ncol(homework_image))) rasterImage(homework_image,0,0,nrow(homework_image),ncol(homework_image),interpolate=TRUE)
displaying each channel of the noised image
par(mfrow=c(1,3)) image(homework_image[,,1],col=rgb(c(0:255)/255,0,0),useRaster = TRUE,axes=FALSE) image(homework_image[,,2],col=rgb(0,c(0:255)/255,0),useRaster = TRUE,axes=FALSE) image(homework_image[,,3],col=rgb(0,0,c(0:255)/255),useRaster = TRUE,axes=FALSE)
plotting the gray image
par(mfrow=c(1,1)) gray_image<-homework_image[,,1] plot(NA,xlim=c(0,nrow(gray_image)),ylim=c(0,ncol(gray_image))) rasterImage(gray_image,0,0,nrow(gray_image),ncol(gray_image),interpolate = TRUE)
dividing into patches
d <- as.matrix(gray_image) ii <- seq(1, (nrow(gray_image)-2), 1) jj <- seq(1, (ncol(gray_image)-2), 1) r <- list()
q <- 1 for (i in ii) { for (j in jj) { r[[q]] <- d[i:(i+2), j:(j+2)] q <- q + 1 } }
r<-t(as.data.table(r[])) rownames(r)<-NULL
pca
pca_image<-princomp(r) summary(pca_image) pca_image$loadings
component1
par(mfrow=c(1,1)) pca_image\(scores[,1]<-((pca_image\)scores[,1]-min(pca_image\(scores[,1]))/(max(pca_image\)scores[,1])-min(pca_image\(scores[,1]))) pca_image\)scores[,1]<-t(matrix(pca_image$scores[,1],510,510))
plot(NA,xlim=c(0,1),ylim=c(0,1)) rasterImage(pca_image$scores[,1],0,0,1,1,interpolate=TRUE)
component2
pca_image\(scores[,2]<-((pca_image\)scores[,2]-min(pca_image\(scores[,2]))/(max(pca_image\)scores[,2])-min(pca_image\(scores[,2]))) pca_image\)scores[,2]<-t(matrix(pca_image$scores[,2],510,510))
plot(NA,xlim=c(0,1),ylim=c(0,1)) rasterImage(pca_image$scores[,2],0,0,1,1,interpolate=TRUE)
component3
pca_image\(scores[,3]<-((pca_image\)scores[,3]-min(pca_image\(scores[,3]))/(max(pca_image\)scores[,3])-min(pca_image\(scores[,3]))) pca_image\)scores[,3]<-t(matrix(pca_image$scores[,3],510,510))
plot(NA,xlim=c(0,1),ylim=c(0,1)) rasterImage(pca_image$scores[,3],0,0,1,1,interpolate=TRUE)
loading1
loading1<-matrix(pca_image$loadings[,1],3,3) loading1<-((loading1-min(loading1))/(max(loading1)-min(loading1))) plot(NA,xlim=c(0,1),ylim=c(0,1)) rasterImage(loading1,0,0,1,1,interpolate=TRUE)
loading2
loading2<-matrix(pca_image$loadings[,2],3,3) loading2<-((loading2-min(loading2))/(max(loading2)-min(loading2))) plot(NA,xlim=c(0,1),ylim=c(0,1)) rasterImage(loading2,0,0,1,1,interpolate=TRUE)
loading3
loading3<-matrix(pca_image$loadings[,3],3,3) loading3<-((loading3-min(loading3))/(max(loading3)-min(loading3))) plot(NA,xlim=c(0,1),ylim=c(0,1)) rasterImage(loading3,0,0,1,1,interpolate=TRUE)